@article {MATHEDUC.06124936,
author = {Ho, Weng Kin and Ho, Foo Him and Lee, Tuo Yeong},
title = {An elementary proof of the identity $\cot \theta = \frac{1}{\theta}\sum _{k=1}^{\infty} \frac{2 \theta}{\theta ^2 - k^2 \pi ^2}$.},
year = {2012},
journal = {International Journal of Mathematical Education in Science and Technology},
volume = {43},
number = {8},
issn = {0020-739X},
pages = {1085-1092},
publisher = {Taylor \& Francis, Abingdon, Oxfordshire},
doi = {10.1080/0020739X.2011.644337},
abstract = {Summary: This article gives an elementary proof of the famous identity $$\cot \theta = \dfrac{1}{\theta} \sum _{k=1}^{\infty} \dfrac{2 \theta}{\theta ^2 - k^2 \pi ^2}, \quad \theta\in \Bbb{R}\setminus \pi \Bbb{Z}.$$ Using nothing more than freshman calculus, the present proof is far simpler than many existing ones. This result also leads directly to Euler's and Neville's identities, as well as the identity $\zeta(2) := \sum _{k=1}^{\infty}\frac{1}{k^2}= \frac{\pi ^2}{6}$.},
msc2010 = {I30xx (I50xx)},
identifier = {2013a.00687},
}